Listen, swapping necks "isn't " as easy as it may seem. Absolutely, you will more than likely have an "intonation" problem even if you do get the neck on.
Putting a neck on a guitar is an "extremely" technical and sensitive issue (to do it right), and encompasses MANY areas of concerns that need to be addressed in the process.
I've plugged and replaced (interchanged) many necks on many different guitars, and I would not recommend it unless you are practicing and tweeking your skills, which is cool and fun.
But remember, the FINAL test when all is said and done, is it going to intonate correctly!!
Sorry dude, in this instance it won't work. But it's only because of the 22/24 fret difference. The petrucci and axis each have different neck pocket sizes, if you were swapping a luke neck on to an axis etc, it would be all good. But sadly this way around, no bingo.
In my experience, assuming you're swapping necks with the same size pocket and dimensions/scale length etc, and I've swapped a few around, you shouldn't encountered too many issues - I've never had any in fact, just a bit of a tweak. But I guess it's all relevant to your own level of expertise/knowledge/comfort zone etc